Introduction to Dynamical Systems and Geometric Mechanics

Title

Introduction to Dynamical Systems and Geometric Mechanics

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Description

This is an introductory graduate text on dynamical systems and geometric mechanics, with applications to physics and engineering. In the first part of the text, we discuss linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the text begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms. The final chapters cover Lagrangian and Hamiltonian mechanics from a modern geometric perspective, mechanics on Lie groups, and nonholonomic mechanics via both moving frames and fiber bundle decompositions.

ISBN

978-0-9850627-0-5

Publication Date

4-2012

Publisher

Solar Crest

City

San Jose, CA

Disciplines

Mathematics

Introduction to Dynamical Systems and Geometric Mechanics

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